Answers should be submitted in an MS Word document. Simulations should accompany answers in a separate MATLAB file.

1) Queuing Simulator: Consider a communications router that can route (service) EXACTLY 800 messages per second (mps).

- Assume that messages arrive at an AVERAGE rate of 850 messages per second.
- Assume that the arriving messages follow an exponential distribution, while the routing (service) times are constant.

a. Develop and submit a MATLAB Monte Carlo Queuing Simulator that will:

- Graphically show the number of messages in the queue as a function of time. Provide a screen shot in this word document.
- In text show the average number of messages in the queue and the average time a message spends waiting in the queue. Provide a screen shot in this word document.
- Note: you will have to modify the MC Queuing simulator attached

b. Run your simulation for the arrival and routing (service) rates indicated above for a total of 4000 messages. Provide a screen shot of the results.

c. Does the queue appear stable from the output? Explain.

d. Does this make sense? Explain. (Hint: look at arrival rates and servicing rates)

2) Queuing Model Questions: Consider a car repair shop a with the following characteristics:

- 6 customers arrive per hour
- 4 mechanics
- Each mechanic is capable of servicing 2 customers per hour
- Assume that arrival times and service times are exponentially distributed.

a. How would you represent the system using Kendall's notation?

b. Calculate:

a. The utilization factor for the system.

b. Is the queue stable or unstable? Why or why not?

c. The average number of customers in the queue.

d. The average number of customers in the system.

e. The average wait time in the queue.

f. The average wait time in the system.

c. What is the probability the 3 or fewer more customers will show up in the first hour?

3) RAM Questions: Consider two years of driving your car.

- You drive an average of 1 hour a day for 300 days a year.
- Over this period of time you have experienced 3 malfunctions that have necessitated taking the car in for servicing.
- When you take the car in for servicing, you spent an average of 3 hours waiting for the car to be repaired.

a. What is the mean time between failures for your car?

b. What is the reliability of your car over a 1 year period?

c. What is the mean down time for your car?

d. What is the availability of your car?